Optimal stability for trapezoidal-backward difference split-steps
The marginal stability of the trapezoidal method makes it dangerous to use for highly non-linear oscillations. Damping is provided by backward differences. The split-step combination (αΔt trapezoidal, (1 – α)Δt for BDF2) retains second-order accuracy. The ‘magic choice’ a = 2 – √2 allows the same Ja...
| Main Authors: | , , |
|---|---|
| 其他作者: | |
| 格式: | 文件 |
| 语言: | en_US |
| 出版: |
Oxford University Press
2013
|
| 在线阅读: | http://hdl.handle.net/1721.1/80879 https://orcid.org/0000-0001-7473-9287 |
| 总结: | The marginal stability of the trapezoidal method makes it dangerous to use for highly non-linear oscillations. Damping is provided by backward differences. The split-step combination (αΔt trapezoidal, (1 – α)Δt for BDF2) retains second-order accuracy. The ‘magic choice’ a = 2 – √2 allows the same Jacobian for both steps, when Newton's method solves these implicit difference equations. That choice is known to give the smallest error constant, and we prove that a = 2 – √2 also gives the largest region of linearized stability. |
|---|